Recovering Initial States in Semilinear Parabolic Problems from Time-Averages
Abstract
Well-posedness of certain semilinear parabolic problems with nonlocal initial conditions is shown in time-weighted spaces. The result is applied to recover the initial states in semilinear parabolic problems with nonlinearities of superlinear behavior near zero from small time-averages over arbitrary time periods.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.03829
- arXiv:
- arXiv:2407.03829
- Bibcode:
- 2024arXiv240703829S
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- 19 pages